Theorem 3 Strategic Behavior) There exists a unique

order conditions established in lemma (c), which is uniquely characterized by:

5

equilibrium of are satisfied20.

the overall Each firm

x ∗ E Q

(c) =

            

0

(x, c) :

X:

  

x0(c) with

=

F(

c EQ

)

1 kc(c)

f(

c EQ

)(n 1)b2x b(F (

c EQ

)

θ c E Q

= c + b(n + 1)x

n

θ∗

(n + 1)bx = c∗

o

1 kc(c))

  

c < c∗

c∗ ≤ c ≤ c∗

c∗ < c.

(20)

Proof

Proof see appendix 8.

dQ

i

dx

i c)

19This ensures that

) is well defined. Similar restriction to di erentiable functions are found in

many contributions of the literature, compare for example the article on supply function competition by

Klemperer and Meyer (1989). 20As stated in lemma 5, the second order conditions are always satisfied if conditions (a), (b) and (c) are

satisfied. Especially the assumption of linear demand was made mainly in order to limit the computational burden when determining second order conditions. The symmetric candidate solution for the nonlinear case however would only change slightly and is given by the following di erential equation: